Visualization

1. Go to https://www.desmos.com/calculator/gwha6ksu9m
2. Examine the expression in line 2, and compare it to Eq. (19) and (20) in section 10.7 of your DiffEq book. In the Desmos calculator expression, note that L and a are chosen to be equal to 1. For the expression in the Desmos calculator, n = 1. When looking at Eq. (20), note that the coefficient c₁ is set to 1. In what remains, all the c_n‘s will be set to 1 (but that is just for convenience and is rarely the actual case).
3. Note the axes on the graph. This is a snapshot of the wave at time t = 0. To see what the wave looks like at different times, use the slider in line 1 to pick different values of t.
4. Now, hit the play button to animate the graphs. After examining for a while, pause the animation.
5. In the line below the expression for u₁, type in an expression for u₂. Compare these two graphs to Figure 10.7.3.
6. Play the animation again. Does u₂ oscillate twice as fast as u₁ as expected?
7. While watching the animation, see if you can imagine what the superposition of the two wave functions would look like. Discuss with your neighbors.
8. Pause the animation.
9. In the next line, type in u₁ + u₂. Play the animation.
10. Pause the animation, and hide u₁ + u₂ by clicking on the colored circle all the way to the left of the line holding the expression.
11. Type in an expression for u₃. Compare the three graphs to Figure 10.7.3.
12. Play the animation again (which should just show the individual graphs). Again, imagine what the superposition of the three wave functions would look like.
13. Modify your u₁ + u₂ to add in u₃, show the graph, and animate it.

Close Reading

1. Go to this editable Google Doc (you don’t need to log into a google account unless you want to).
2. Read the instructions on the first page, and then proceed.